Lab 6 Phy 111

docx

School

University Of Arizona *

*We aren’t endorsed by this school

Course

111

Subject

Mechanical Engineering

Date

Jan 9, 2024

Type

docx

Pages

Uploaded by nicolejj20

Nicole Jauregui PHY 111 Section: 25902 November 20, 2023 Lab 6 – Uniform Circular Motion Lab Purpose: The purpose of this lab is to analyze the relationship between the centripetal (net) force acting on an object and the rotational speed of that object. Materials: Straw, string, paperclips (2), washers, ruler, stopwatch, lab assistant (optional) Procedures: 1. To begin you must first cut a piece of string that is 1.0 meter long. 2. Run the string through the straw. 3. Then, tie two of the washers to the top end of the string and then tie a paperclip to the bottom end of the string. 4. Slide five washers onto the paperclip. 5. Make sure the second paperclip is fastened to the string below the straw. This is to not let the paperclip come in contact with the straw. Then, tie a knot onto the string below the straw. 6. Then you will need to measure the length of string between the two washers and the straw as this will be your radius of rotation and value should remain constant for all trials. 7. Holding the straw, spin the two washers over your head in a horizontal circle parallel to the ground. 8. Assure that the paperclip attached to the string below the straw remains without touching the straw during the entire rotation. This may take practice. 9. Measure the time of two washers to preform 10 revolutions. 10. Repeat this trial run as you will average the results. 11. You will then add five more washers to the bottom paperclip and measure the time for two washers to preform 10 revolutions. 12. Repeat this trial run as you will also average the results. 13. Continue to add washers to the bottom paperclip for a total of five more trials. For each trial, add 2 or 3 washers at a time until on the final trial all washers are used. Each one of these trials should have at least one repetition. 14. You will then calculate the period for each trial. 15. Calculate the average period for each trial. 16. Calculate the rotational speed for each trial. 17. Calculate the centripetal force acting on two washers for each trial. 18. Create a graph of centripetal force vs. speed. Force should be on vertical axis.

Nicole Jauregui PHY 111 Section: 25902 November 20, 2023 Photographs: Data: Trial 1 2 3 4 5 6 # of washers 5 10 12 14 16 18 Repetition 1 (sec) 8.12 6.75 6.68 6.45 6.28 5.62 Repetition 2 (sec) 7.50 6.92 6.45 6.28 6.12 5.64 Time for 10 Revolutions (sec) 7.81 6.84 6.57 6.37 6.20 5.63 Average period of trials (sec) 0.781 0.684 0.657 0.637 0.62 0.563 Rotational Speed (m/s) 4.95 5.65 5.88 6.07 6.23 6.86 Centripetal force (N) 0.211 0.421 0.506 0.59 0.674 0.759 Length of radius of string: 0.615 m

Nicole Jauregui PHY 111 Section: 25902 November 20, 2023 Calculations and Graphs: Calculation Equation Plug-in Solution Period Time for one rotation= (recorded time)/ (Number of rotations) 7.81 sec /10 0.781 sec Average Period Tavg=(T1+Trepetition)/2 (8.12 sec + 7.50 sec)/2 7.81 sec Rotational Speed (velocity) V= (2pir)/Tavg (2pi*0.615 m) / 0.781 sec 4.95 m/s Centripetal force SumFx=W=mg (0.0043 kg*5)* 9.8 N/kg 0.211 N % difference (|Measure 1 - measure 2|/avg of measurements)x100 (|8.12- 7.50|/7.81x100 7.94% 4.5 5 5.5 6 6.5 7 7.5 8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 f(x) = 0.26 x − 1.04 Centripetal force vs. Speed Velocity (m/s) Force (N) Results: The trendline y= 0.262x-1.042 shows that there is a linear relationship between centripetal force and rotational speed. The graph shows that as the rotational speed increases, the centripetal force also increases making this a positive relationship. Conclusion: Theory/Background As the purpose of this lab was to analyze the relationship between centripetal forces and rotational speed, centripetal force refers to any net force that is causing uniform circular motion.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Nicole Jauregui PHY 111 Section: 25902 November 20, 2023 This topic comes in hand with Newton’s second law of motion as the direction of centripetal force is the same as the direction of centripetal acceleration. So, as the rotational speed increases, the centripetal force required to keep the object in its circular path will increase if radius is kept constant. This relationship is crucial in understanding the dynamics of objects moving in circular motion. Interpretation of Results The slope of our trendline on the graph is y=0.262x, a positive slop suggests that there is proportionality between the two variables. As rotational speed increases by one unit, the centripetal force increases by 0.262 units. Proving that as speed increases, the centripetal force also increases. The y-intercept represents the value of centripetal force when the rotational speed is zero. This means that a rotational speed of zero implies no motion. Sources of Error One possible source of error could be an error with precision when gathering the data points as I calculated percent differences of my data. According to my calculations, I was not precise during the first trial as I obtained a percent difference of 7.94%. In my second trial I obtained a percent difference of 2.49%, and my third trial 3.67%. Although these percent differences are low, they are still significant because it shows that my data is not internally consistent. A specific source of error could be when my lab partner was helping me with the stopwatch. Since my lab partner would begin the stopwatch when both washers began to move and then stopped when I had made the 10 rotations over my head, there could be a precision error there. There could have also been some inconsistency in spinning as this variability in force could affect the centripetal force measurements. Finally, another possible source of error could have been friction between the string and the straw, as it could create resistance, affecting the motion of the washers. Analysis 1. Look up the equation for centripetal force in your book. Does this equation match your graph relating centripetal force and speed? - Centripetal force equation in the book Is Fc=mrw^2. This equation does match my graph relating to centripetal force and speed as the mass of an object is referred to as ‘m’ in the equation. In my experimental setup, the mass of the washers is likely the correspondance. The radius of circular motion is represented by ‘r’ in the equation. The length of the string between the washers and the straw is my radius of rotation. The equation pulls everything together is describes that as the speed of the object increases, the centripetal force also increases and vice versa.

Nicole Jauregui PHY 111 Section: 25902 November 20, 2023 References Urone, P. P., & Hinrichs, R. (n.d.). Ch. 1 introduction to science and the realm of physics, physical quantities, and units - college physics . OpenStax. https://openstax.org/books/college-physics/pages/1-introduction-to-science-and-the-realm- of-physics-physical-quantities-and-units Urone, P. P., & Hinrichs, R. (n.d.-b). 6.3 Centripetal Force - College physics . OpenStax. https://openstax.org/books/college-physics/pages/6-3-centripetal-force Lesson 6 - Uniform Circular Motion . Lesson 6 - Uniform Circular Motion: Section 6.1 - Centripetal Force. (n.d.). https://riosalado.coursearc.com/content/phy111-in-v5/lesson-6- uniform-circular-motion/section-61-centripetal-force